Answer:
C. 38.25%
Step-by-step explanation:
We know that,
[tex]\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right][/tex]
here,
PV = Present value of annuity = $1,874
P = Payment per period (monthly)
r = Rate of interest per period = 10.31% annually = [tex]\dfrac{0.1031}{12}[/tex] monthly
n = Number of periods = 4 years = 48 months
Putting the values,
[tex]\Rightarrow 1874=P\left[\dfrac{1-(1+\frac{0.1031}{12})^{-48}}{\frac{0.1031}{12}}\right][/tex]
[tex]\Rightarrow P=\dfrac{1874}{\left[\frac{1-\left(1+\frac{0.1031}{12}\right)^{-48}}{\frac{0.1031}{12}}\right]}[/tex]
[tex]\Rightarrow P=\$47.81[/tex]
So the monthly payment is $47.81, then the total payment will be,
[tex]=47.81\times 48=\$2294.88[/tex]
Over the eight years that Olivia kept the sprinkler system, it used an average of $2.11 in water per week.
The total amount will be,
[tex]=2.11\times 52\times 8\\\\=\$877.76[/tex]
Then the percentage of the total lifetime cost of the system did the original price make up is,
[tex]=\dfrac{877.76}{2294.88}\times 100\%[/tex]
[tex]=38.25\%[/tex]
Answer:
b.
59.07% on edge anyway i took the test
Step-by-step explanation:
